Empirical Rule & Z-Score

In a normal distribution, what percent of the values lie above the mean?

• 13.5%

• 34%

• 50%

• 68%

The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees.  What is the z-score for a temperature of 17 degrees?  

• 1 

• 1.43

• -1.43

• 11.5

At a recent invitational, Emmett ran the 400 in 53.5 seconds with an invite mean of 51 and a SD of 3. Reese ran the 800 in 2 minutes, 1 second with the mean being 2 minutes 46 seconds and SD of 15 seconds. What were their Z-scores and who performed better?

• Emmett's Z-score was +0.83, Reese's was -3.0. Emmet did better

• Emmett's Z-score was +0.83, Reese's was -3.0. Reese did better because in track lower z-scores are better.

• You can't tell since it's two different events.

• Mr. McDonald can smoke both of 'em.

The average waist size for teenage males is 29 inches with a standard deviation of 2 inches.

If waist sizes are normally distributed, determine the z-score of a teenage male with a 37.5 inch waist.

• 4.25

• 1

• -2

• -1

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What ACT score is 3 standard deviations below the mean?

• 12

• 16

• 20

• 21

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5.

What percent of scores are between 65 and 75?

• 34%

• 50%

• 68%

• 81.5%

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What percent of ACT scores are between 20 and 28?

• 34%

• 68%

• 81.5%

• 95%

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What percent of ACT scores are between 16 and 24?

• 34%

• 47.5%

• 49.85%

• 50%

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 99.7% of molds filled by this machine will hold weights in what interval? 

• 1084 to 1216 pounds 

• 1106 to 1150 pounds 

• 1106 to 1194 pounds 

• 1128 to 1172 pounds

What percent of people within 3 standard deviations of the mean?

• 99.7

• 34

• 68

• 95